Originally Posted by base2

The shifters & the derailleurs need to have matching pull ratios. Having a "group set" is just a convenient means of catagorizing use cases.

Shimano 8,9,10 speed road/mountain rear derailleurs are interchangeable. Most people make the switch to mountain rear derailleurs for the additional capacity & larger mountain cogs. So the "9" of the 3x9 shifters I suggested is a "Go."

The front derailleurs are not always interchangeable. There are definite road fronts & mountain fronts. It depends on the vintage & group set. Others here would have more authority on the specifics than me. What I do know is it's easiest to match the front derailleur to the front shifter & save the compatibility trouble.

In this case, you specify you want a road brifter. So: road Claris, Sora, 105, or Ultegra, "triple" derailleurs are your options. All ought to work with the "3" of the 3x9 shifters I suggested above. So you are a "Go" there as well.

The crankset is built around a particular bottom bracket width. The spacing between the rings & chainline is the same. The primary difference is mountain has a smaller tooth counts across the board. But a tooth or 2 difference in gear diameter is insignificant as far as derailleur height/cage curvature is concerned. So buy the triple crankset that suits your fancy.

Where you often run into fitment issues is puting doubles on (68mm) mountain frames...They exist, & there is a lot out there. The larger diameter rings or narrower crank arm q-factor sometimes causes issues hitting the chain stays. It's seldom an issue going the other way.

If you have an issue with the triple road crank arms from a triple road crankset hitting the chainstays, you may be forced into a mountain triple crankset to move the pedals/crankarms wider...but I don't think that'll be an issue.